Dave,
If the wheel is vibrating then there is something amiss. There should be plastic spacers to hold the wheel on centreline and paper pads for the sides of the wheel. You should not have to dress the wheel for true from new, if it is that far out then send it back as it is faulty.
Vibrating wheels can shatter and cause serious injury…..
As mentioned earlier, "ringing" of the wheel is necessary to check for cracks…….hold the wheel by one finger through the hole and tap the wheel with a knuckle quickly NOT a hammer. If the wheels rings it is good, if it is dull then it is cracked and should be binned or dropped on the floor and broken to prevent anyone else using it.
Grinding wheels are far more dangerous than they appear so don't take chances…..
Green grit wheels are ok but don't last long on carbide, but are cheaper than diamond wheels. The price you pay will depend on how often you are likely to use it.
trevor